Existing accounts of student thinking about mechanical wave propagation and superposition emphasize that students sometimes treat wave pulses as objects, saying, for example, that pulses bounce off of one another when they meet. In this paper, we present a context in which students explicitly reason about pulses as not-objects, instead describing…

This case study demonstrates the ability of high school chemistry students, with varying levels of math preparation, to experience learning-gains on state and district assessments as it relates to chemical reactions, thermodynamics, and kinetics. These advances were predicated on the use of a teaching style rooted in abstract reasoning. The…